We have one team providing an example of school teams keeping contact, not enough to say heavy implication.
the leading theory is that hunters are government employed to some degree, and as such are likely sent out on missions as a military asset.
Next, a group of hunters being deployed as a unit after graduation would not need to follow the team names used by schools, and would likely follow a more standard military naming convention.
Finally, Zugzwang, why are you using RWBY setting if you are disregarding everything but terminology? why not reskin it and give yourself more freedom? that way you can use the basics and not worry about things like CNR and team naming conventions.